Deform Blast Bags on Ship Turret when moving the barrels
Given the restricted range of movement required, a physics/cloth simulation might be a bit over the top? Maybe a 2-bone armature will do.. The joint between the bones is at the center of rotation of the barrel.

The root bone could be a child of the turret, the barrel-bone constrained to point down the barrel. You could start with automatic weights, and tweak in weight-painting to something like this:


Barrel Bone





Root Bone




If you want to introduce folds in the fabric, you can use corrective shape-keys. There is one in this animation, but only to suppress unnatural bulging...

If you haven't rigged to an armature before, I wish I could give a complete description in one BSE answer, but it would be too broad. Maybe check out some basic tutorials (not bothering about Inverse Kinematics to begin with), and if you get stuck on a particular step, call back with another question. This isn't a bad starting exercise.